We rigorously prove a central limit theorem for neural network models with a single hidden
layer. The central limit theorem is proven in the asymptotic regime of simultaneously (A) …

Machine learning, and in particular neural network models, have revolutionized fields such
as image, text, and speech recognition. Today, many important real-world applications in …

We discuss the construction and approximation of solutions to a nonlinear McKean–Vlasov
equation driven by a singular self-excitatory interaction of the mean-field type. Such an …

This article surveys models of counterparty contagion and their application in systemic risk
management, emphasizing the network of counterparty relationships. It addresses how …

We prove a law of large numbers for the loss from default and use it for approximating the
distribution of the loss from default in large, potentially heterogeneous portfolios. The density …

We introduce a simple class of mean-field games with absorbing boundary over a finite time
horizon. In the corresponding N-player games, the evolution of players' states is described …

We propose a dynamic mean-field model for 'systemic risk'in large financial systems, derived
from a system of interacting diffusions on the positive half-line with an absorbing boundary at …

Financial institutions, government-sponsored enterprises, and asset-backed security
investors are often exposed to delinquency and prepayment risk from large numbers of …

We develop a mean field model of interbanking borrowing and lending activities. Each bank
borrows from or lends to other counterparties at an idiosyncratic rate and is exposed to …

We consider a mean field game describing the limit of a stochastic differential game of N-
players whose state dynamics are subject to idiosyncratic and common noise and that can …